Pricing-to-Market and the Failure of Absolute PPP

By George Alessandria and Joseph P. Kaboski∗

Abstract: We show that deviations from the law of one price in tradable goods are an important source ofviolations of absolute PPP across countries. Using highly disaggregated export data, we document systematicinternational price discrimination: at the U.S. dock, U.S. exporters ship the same good to low-income countriesat lower prices. This pricing-to-market is about twice as important as any local non-traded inputs, such asdistribution costs, in explaining the differences in tradable prices across countries. We propose a model ofconsumer search that generates pricing-to-market. In this model, consumers in low-income countries have acomparative advantage in producing non-traded, non-market search activities and therefore are more pricesensitive than consumers in high-income countries. We present cross-country time use evidence and evidencefrom U.S. export prices that are consistent with the model. (JEL E31, F12)

Keywords: PPP, Pricing-To-Market, Law of One Price.

[INSERT FIGURE 1 HERE]

Figure 1 plots income per capita against the consumer price level and draws a line with the

estimated magnitude of this relation for the benchmark countries in the Penn World Tables. This

picture raises two questions: First, why are there large differences in consumer price levels across

countries? The theory of absolute Purchasing Power Parity (PPP) states that the same basket of

goods should sell for the same price everywhere, yet, for instance, the price level in Mexico is 64

∗Alessandria: Research Department, Federal Reserve Bank of Philadelphia, Ten Indepedence Mall,Philadelphia, PA 19106 (george.alessandria@phil.frb.org); Kaboski: Department of Economics, 434 FlannerHall, University of Notre Dame, Notre Dame, IN 46556 (jkaboski@nd.edu). Alessandria thanks the NationalScience Foundation for financial support. Kaboski thanks the National Institute of Health and The Ohio StateUnivesity for financial support. This paper is a substantially revised version of the working paper, “ViolatingPurchasing Power Parity.” The authors thank two anonymous referees, Andy Atkeson, Ariel Burstein, MarioCrucini, Marvin Goodfriend, Patrick Kehoe, Fabrizio Perri, Kim Ruhl, Bruce Weinberg, and Kei-Mu Yi forhelpful comments. Virgiliu Midrigan and Jarcy Zee provided excellent research assistance. All remainingerrors are our own. The views expressed here are those of the authors and do not reflect the views of theFederal Reserve Bank of Philadelphia or the Federal Reserve System.

percent of the price level in the United States.1 Second, why are price levels so strongly related to

income per capita? A doubling of income per capita is associated with a 48 percent higher price

level.2 The conventional explanation for these two observations is the model of Roy F. Harrod (1933),

Bela Balassa (1964), and Paul Samuelson (1964), the HBS model hereafter. In HBS, differences in

price levels are driven solely by non-tradable goods, for which the law of one price (LOP) doesn’t

hold. Since the LOP holds for traded goods, international relative wages are determined by the

large productivity differences in tradables. Large differences in wages lead to differences in the

price of non-tradables, a sector in which productivity differences are much smaller across countries.

The model therefore rests on the assumption that cross-country productivity differences are much

smaller in non—tradables than in tradables, and that the LOP holds in tradables.3

[INSERT FIGURE 2 HERE]

There are two good reasons to doubt HBS as a full explanation of these observations. First,

we see from Figure 2, which plots the price levels of tradable consumption goods against income per

capita, that the LOP for tradables is clearly violated in the data. As in Figure 1, the relationship

between prices and income is positive and significant, and the estimated elasticity in tradables

(0.31) is nearly two-thirds of the overall elasticity (0.48).4 Second, to explain the magnitude of the

relation in Figure 1, the rise in relative productivity of tradables with income across countries (the

cross-section) would have to be much bigger than what we observe within countries (the time series).

The aim of this paper is to evaluate the role of systematic price discrimination across coun-

1Kenneth Rogoff (1996) provides a review of PPP.2We focus here on consumer prices, which is commonly the focus in the literature on PPP. Similar relationships

hold when looking at all final goods, however, with elatisticities of 0.43 overall and 0.26 for tradables.3A few existing theories present alternatives to HBS. Irving Kravis and Robert E. Lipsey (1983) and Jagdish N.

Bhagwati (1984) focus on differences in factor endowments. Staffan B. Linder (1961), Rudiger Dornbusch (1988), PeterNeary (1988) and Jeffrey H. Bergstrand (1991) focus on differences in preferences. All of these theories assume thatthe LOP holds for tradables.

4These deviations from PPP are quite persistent. Of the countries with price levels less than half the U.S. level in1996, over 80 percent (26 out of 32 available in 1985) also had price levels less than one-half that of the U.S. in 1985.These countries also had very low income, with GDP per capita on average 14 percent of the U.S. level in 1996.

1

tries, what Paul Krugman (1987) calls pricing-to-market, in the pattern of tradable and overall

price levels in Figures 1 and 2. The tradable price variation in Figure 2 could be interpreted as

direct evidence of pricing-to-market, but a potential problem is that tradable prices are measured

using final goods prices. Thus, differences in retail prices may be driven by non-traded components,

such as transportation and distribution, instead of differences in the actual price of tradables earned

by the producer. Additionally, despite the best efforts of statistical agencies to compare identical

goods, there may be quality differences between goods in different countries. Ideally, to overcome

such data concerns requires micro price data on identical products in multiple countries. Such data

is generally only available for a few goods (see Ina Simonovska, 2008, for some clothing products in

Europe) and is suggestive. Clear examples of a good where the exporter price discriminates based on

the destination market are submission fees to AEA journals, including this journal. Submission fees

vary from $0 to $100 ($0 to $200 for non-members) depending on the country where the submitter

works. Similarly, membership fees vary positively with income with a significant elasticity 0.06.5

Evaluating the role of pricing-to-market in aggregate PPP requires broader data, however.

We examine unit values of the universe of U.S. exports, data for which the above concerns are

(partially) mitigated. In particular, the data are well-suited for isolating pricing-to-market because

they are highly disaggregate, and they measure the export income received at the U.S. border before

any local non-traded inputs are added. The data show that unit values are higher for exports to

high-income countries. On average, the richest country in our data set pays 48 percent more per

unit than the poorest country. These results appear robust to controls for quality differences and

suggest price discrimination is common. The estimated elasticity of price with respect to GDP

per capita is 0.22, indicating that about two-thirds of deviations in the LOP in final tradables

5We cannot estimate a similar pricing-to-market coefficient for submissions, since submissions from low incomecountries are free. However, restricting ourselves to countries with positive submission fees we find a pricing-to-market coefficient of 38 percent. Details of our analysis of AEA subscription and membership prices are given in theunpublished web appendix.

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could be due to pure pricing-to-market. Thus, this data show that the tradable price vs. income per

capita relationship from Figure 2 may primarily reflect pricing-to-market rather than the non-traded

content of tradable goods.

What characteristics of consumers or markets might lead firms to price discriminate based on

income? The second aim of this paper is to propose a strong candidate for a micro-level explanation

for higher elasticities of demand from consumers in low-wage countries. In Section II, we develop a

model based on consumer search frictions and international productivity differences. Search requires

time, which consumers in high-productivity/high-wage countries value at a premium. They are

therefore less willing to search and less price elastic shoppers. Firms take this into account and set

relatively high prices (and therefore markups) when selling to high-wage countries. Thus, there is a

tight (endogenous) link between the local wage and prices, both tradable prices and non-tradable

prices. Our consumer search story parallels and complements the HBS story. That is, we too rely

on small differences in the productivity of a non-traded good. The search friction story requires that

productivity in shopping rises less rapidly with income than productivity in market production.

Our focus on search as the source of pricing-to-market is motivated by the substantial evidence

that search matters for explaining how prices vary by income within countries. Time-use studies

find that poorer consumers, and those with a lower opportunity cost of time, spend relatively more

time shopping per purchase (David McKenzie and Ernesto Schargrodsky, 2005, and Mark Aguiar

and Erik Hurst, 2007). Furthermore, these studies find that shopping time is negatively related

to purchase price, a direct implication of the search model. This effect is potentially large within

countries. For instance, Aguiar and Hurst find, using scanner data on prices paid and time-use

data on shopping time, that a doubling of search effort lowers the expected purchase price by 7 to

10 percent. Our search model can generate a similar relationship within countries, but because in

general equilibrium firm pricing responds to an elastic demand, we get much larger effects across

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countries. For this reason, search is a quantitatively important source of pricing-to-market. A key

advantage of our approach is that it offers a simple, unified theory to explain price dispersion within

and across countries.

In Section III, we conduct a quantitative analysis of the search model. We find the model

can account for about half of the observed pricing-to-market relationship, and 51 percent of the

PPP-income relationship, or about twice as much as the HBS model alone explains. The existence

of pricing-to-market augments the HBS explanation in two ways. It helps reconcile the smaller

observed differences in the relative price of tradables to non-tradables, and it also helps reconcile

large differences in average price levels with the evidence that relative productivity in the tradable

sector does not increase nearly as much with income (in the time series) as the HBS explanation

would require (in the cross-section of countries). Finally, if our model captures the main source of

pricing-to-market, then the difference between our model’s quantitative results and our empirical

findings using export data suggest that quality variation accounts for at most one-half of the price-

income relationship in the export data.

Further corroborating evidence, which we review, supports the consumer search model as

a strong candidate explanation for the pricing-to-market we observe. First, we show, using cross-

country time-use studies, that the ratio of shopping time to work time increases substantially with

income, which indicates that shopping productivity does not increase as rapidly as income (and

overall productivity). Second, our U.S. export evidence shows that the opportunity cost of time

(wage) is more robustly associated with prices than with income, and that pricing-to-market is

strongest for consumer goods. Finally, quantitatively, numerical examples indicate that the search

model can potentially generate pricing-to-market of the order observed in the U.S. export data.

In addition to contributing to the study of absolute PPP, this paper relates to two other

literatures. Our emphasis on pricing-to-market in tradables as an important source of violations from

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absolute PPP is consistent with the prevailing view in the literature on relative PPP. Charles Engel

(1999) and V. V. Chari, Patrick J. Kehoe and Ellen McGrattan (2002) show that deviations from the

LOP in tradables account for nearly all of the fluctuations in real exchange rates among developed

countries.6 Theoretical explanations of this pricing-to-market take two forms. The first approach

focuses on the role of sticky prices set in local currencies, while the second emphasizes that local

market conditions differ across countries and time so that firms have incentive to systematically price

discriminate internationally.7 Since we are looking at absolute PPP and long term deviations, we

follow the approach of focusing on local market conditions. This paper also relates to the literature

on the role of relative prices and productivities in capital accumulation and growth. Jonathan

Eaton and Samuel Kortum (2001) and Chang-Tai Hsieh and Peter J. Klenow (2007) demonstrate

that relative price differences across countries are important in explaining cross-country variation in

capital stocks and income levels. Hsieh and Klenow therefore argue that understanding the origins

of these relative price and productivity differences is essential. We argue that pricing-to-market,

and not only relative productivities, plays a role in the prices (of investment, for example) that

countries face.

I Pricing-to-Market: Empirics and Importance

In this section, we document evidence, using highly disaggregated data on U.S. exports, that

U.S. firms systematically price discriminate by the income of the destination market. We show that

this price discrimination is not likely due to unobserved quality differences, and that it provides

some evidence for a search model where the elasticity of demand varies with the opportunity cost of

6Patrick Asea and Enrique Mendoza (1994) find the HBS model can not explain real exchange rate and outputfluctuations.

7Starting with Krugman (1987), the local market condition models have sought to explain differences in elastic-ities of demand across countries from first principles without resorting to differences in tastes. A variety of localmarket condition models exist and emphasize both supply considerations, such as differences in industry structure(Rudiger Dornbusch, 1987), and demand considerations, such as the decisions of firms to build market shares (GeorgeAlessandria, 2004).

5

search. Finally, using a modified version of Engel’s (1999) decomposition of real exchange rates, we

find that pricing-to-market accounts for 40 percent of the aggregate price-income relationship and

the non-traded component of final goods accounts for 20 percent.

A. Export Data

The micro data we analyze, U.S. Exports Harmonized System data (see Robert Feenstra et

al., 2002), have significant advantages over the aggregate data in identifying pricing-to-market in

tradables.

First, the data are comprehensive of all U.S. domestic exports (excluding re-exports) and

therefore include only tradable goods. We focus on consumer goods but also present evidence for

a much broader range of tradables. We have annual data on the total value and quantity of all

commodities exported by destination country. We link these data to income per capita data from

the PennWorld Tables 6.1 for the years 1989-2000 and to hourly (manufacturing) wage data available

from the BLS. These wages are reported in nominal local currency, which we convert to international

Geary-Khamis dollars using the PWT PPP price level.8

Given our emphasis on search and the opportunity cost of time, we focus on countries for

which both hourly wage and income per capita data are available. These 28 countries include most

long-term members of the OECD plus Hong Kong, Israel, South Korea, Mexico, Singapore, Sri

Lanka, and Taiwan. Over the 12 years of annual data, we have 1.1 million good-year observations

for these countries, constituting 78 percent of the value of U.S. exports.

The second crucial advantage of this export data is that they are collected “at the dock”

of the U.S. That is, our export prices are based on free-alongside-ship values,9 so they do not

8Converting to U.S. dollars using exchange rates produces nearly identical results, except that estimated elasticitiesof prices are smaller with respect to exchange rate-based income per capita, given their larger variance.

9The free-alongside-ship value is the selling price or cost if not sold, including inland freight, insurance, and othercharges to the U.S. port of export, but excluding unconditional discounts and commissions. It is essentially the pricereceived by the exporting country before shipment.

6

include transportation costs, tariffs, or distribution and retailing costs in the importing country.

One complication, however, is that we do not directly observe prices. Instead, we calculate unit

values from data on the total value and quantity sold. Numerous important studies of deviations

of the LOP and pricing-to-market are based on unit values (see Peter Isard, 1977, Robert Feenstra,

1989, and Michael Knetter, 1993). Unit values have the advantage of providing a measure of

destination-specific prices for a large number of products.

A common concern with unit values is that they may combine goods of different qualities.

These concerns are mitigated somewhat since we are using quite disaggregate data. Indeed, we have

10,741 products classified using the 10-digit Harmonized System product codes. (The appendix

lists 10 randomly selected goods as an example of the level of detail. A broader random sample is

given in our unpublished web appendix.) Nonetheless, quality variation remains a concern, and we

consider possible biases below.

B. Pricing-to-Market Evidence

For exposition, consider a monopolist selling an identical good in different markets (e.g.,

countries). Facing different demand in each market, the firm will, in general, charge price p equal

to a market-varying markup μ over a common marginal cost c. Hence, while marginal costs and

markups may vary across goods, i, and time, t, markups also vary across destination market, j:

ln pijt = ln cit + μijt.

The purpose is to examine whether μijt, the markup charged on good i at time t to destination

country j, is related to the level of income per capita or wages of that country. We estimate the

7

following regression equation:

(1) ln pijt = αit + β ln yjt + eijt,

in which yjt is a measure of destination country income (either GDP per capita, wage, or a vector

of both). The intercepts, αit, capture variation in ln cit. They are estimated as fixed effects for each

good-year combination. We use the “within” estimator, so that the identification of β comes from

variation in the income of destination countries within good-year cells.10 We report White robust

standard errors that allow for heteroskedasticity in eijt, and also allow for country-year clustering.11

Table 1 presents the estimated β coefficients on log income and/or log wages from these fixed-

effect regressions. In these baseline estimates, we focus on consumer goods and automotives, whose

effect on the cost of consumption goods is most direct, but we present results for other types of

traded goods in the next two subsections. The “GDP per Capita Only” estimate, from a regression

where log GDP per capita is the only regressor (in addition to the fixed effects), yields an elasticity

estimate of 0.235 on PPP income/capita. The “Wage Only” estimates are slightly smaller at 0.209.

Both sets of estimates are highly significant, but when we include log wages and log GDP per

capita together in the same regression, log wages wins the horse race hands down. These estimates

are presented in the right-most column. The estimated coefficient on wages remains at nearly the

same level (0.188) and is highly significant, while the GDP per capita coefficient estimate becomes

much smaller (0.041) and insignificant.12

Based on the estimates in Table 1, the magnitude of the price-wage relationship is potentially

large. In 2000, the difference in log wages between the richest and poorest countries in the data set

10Marginal costs are made both good- and year-specific to avoid problems with changing quality over time andissues of non-stationarity in income and prices.11Clustering on good-year has a minor effect on standard errors with the nearly 40,000 good-year combinations.12 Including measures of trade costs such as distance, tariffs, and downstream distribution costs does not substantially

alter our estimates.

8

(Germany and Sri Lanka, respectively) was 2.4 measured in PPP terms. Hence, the implied price

differences in U.S. exports to these countries would be 50 percent.

C. Quality

We interpret the unit value-income relationship we observe as pricing-to-market. Although

the data are extremely disaggregated, one might still suspect that the positive relationship uncovered

is driven by unobserved quality variation.13 That is, perhaps our measured relationship simply

reflects (in part or in whole) a tendency for wealthy countries to import higher quality (and higher

priced) goods within the 10-digit commodity categories. Indeed, variation in import prices at the

same level of aggregation has been attributed to such quality variation (see Peter Schott, 2004,

and Juan Hallak, 2006). Unlike imports though, the quality variation in our data is mitigated

somewhat since exports are from a single source country. Nonetheless, definitively distinguishing

between price discrimination or quality differences requires price data such as what we observe for

AEA memberships and submissions. Lacking such data for a broad set of goods, here we propose

a number of tests that control for quality variation somewhat, and the results suggest that some of

the observed pricing-to-market relationship may indeed result from price discrimination.

Our first approach follows Schott (2004) by using variation in unit values of imports within

an HS-10 category as a measure of the extent of quality variation within the category.14 Specifically,

we define quality variation at the HS 10 level (for a particular year) as the standard deviation of ln

unit values (σj) across all sources. This follows the convention in the literature that attributes price

variation to quality variation. This convention is clearly at odds with the within-country evidence

13 In addition to quality as a potential non-PTM explanations, we also evaluated whether the relationship couldbe driven by transfer pricing among related party trade, and the evidence did not support this. We also consideredwhether pricing might be driven by intellectual property protection and local competition from pirated goods. Ourresults were robust to inclusion of indexes of intellectual property protection.14We considered a variety of alternate approaches to controlling for quality. For instance, we dropped those product

categories viewed as potentially most heterogeneous such as those commodities with descriptions containing wordslike “other,” “not elsewhere specified or included,” “NESOI,” and “parts.” The elasticity estimates are quite similarto the full sample. For instance our full sample estimate in Table 2 falls from 0.159 to 0.149.

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of price variation unrelated to quality variation, however. Additionally, this measure is likely to

overstate quality variation as prices may also be dispersed, if costs are dispersed and producers

have market power. In Table 2, we report pricing-to-market for goods with low quality variation

and high quality variation, where goods have been divided by their dispersion in import unit values

relative to the median σj . Our measure of pricing-to-market indeed increases with quality variation

from 0.128 to 0.183, but the increase is small relative to the increase in quality; in the import data,

those goods with high quality variation have nearly 2.5 times the average quality-driven unit value

variation compared to low quality variation goods (σ of 1.92 vs. 0.78). Moreover, looking at the

10 percent of goods with the least quality variation (σj < 0.46) we still find substantial pricing-to-

market coefficient of 0.107.15 Finally, we can also run a simple regression of prices on wages that

includes an interaction term with our quality measure (σj · wij) of

(2) pij − pj = β0 (wij − wi) + β1σj · (wij − wi) + εij ,

where pj (wi) is the average price (wage) across destinations. The coefficient on wages, β0, here

measures pricing-to-market on goods with no quality variation. Controlling for quality in this way

yields a pricing-to-market coefficient of 0.084 or more than half the overall sample of 0.159. Thus,

using a conventional measure of quality variation we still find substantial pricing-to-market.

A second approach is to further disaggregate the data by port and month of export. The

presumption here is that goods sold from the same port in the same month are more likely to be

from the same supplier and hence more likely to be of similar quality. A key caveat to this analysis is

that ports may differ in their mode of transport (air, ship, truck, rail) and destinations and so some

of the variation in shipments by ports is economically meaningful. Additionally, we do not have a

15Goods with this dispersion in unit values (σj < 0.46) have substantially less systematic variation in unit valuesrelated to the real wage of the source country compared to all goods. For instance, regressing unit values on sourcereal wages yields a coefficient of 7.8 percent for low dispersion goods and a coefficeint of 66 percent for all imports.

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theory of the timing of shipments,16 and so it is not clear one wants to distinguish between monthly

and annual purchases, particularly if, say, low income countries are more sensitive to price variation

over the year. Nonetheless, we run our same regressions on monthly unit values of exports in two

years, 1998 and 1999, but now defining goods at the port-month level. We also include a control

for the number of transactions (to pick up volume discounts) and share of exports by air. Table

3 presents this result, which yields an elasticity of 0.096. Our estimated elasticity is remarkably

stable whether we group goods by port-month, commodity-month, port-year or commodity-year

(estimates range from 0.082 to 0.096) or whether we aggregate observations by port over the year

(0.085). Aggregating observations within a port over a year yields a similar estimate of 0.081. One

should be cautious when comparing this monthly-port estimate to the estimate from the aggregated

annual data as the samples are inherently different (indeed we have 1,753,642 groups of goods at

the port-month level and 15,083 groups at the commodity-year level). Goods that are traded more

frequently will be weighted more in our monthly sample.17 In sum, with even more disaggregate

data we still find sizeable pricing-to-market.

Our third and final approach to controlling for quality directly considers the quality bias

in the data. In particular, the quality explanation for pricing-to-market essentially argues for an

aggregation bias in which 10 digit categories are made up of different 11 digit goods that differ by

quality and price, with rich countries buying relatively more of the relatively high quality and high

price 11 digit goods than poor countries. Obviously we can not sign this bias from the 11 digit to 10

digit level; however, we can sign it at different levels, say from the 10-digit to 9-digit, or 10-digit to

8-digit and so on to examine the strength of the bias. (A formal justification of this approach, based

16For such a theory of the frequency of imports based on fixed ordering costs and inventory management see GeorgeAlessandria, Joseph Kaboski, and Virgiliu Midrigan (forthcoming).17Aggregating goods by commodity, at the monthly level we find a coefficient of 0.148 while at the annual level it

is 0.112. Eliminating the controls for frequency of shipment and mode of transport raise the elasticity to 0.184 at theannual level.

11

on a Lancasterian model where each Harmonized System digit represents a characteristic with a

given price, and an explicit statement of the potential quality bias are developed in the unpublished

web appendix.)

Table 4 reports the results of our aggregation exercise and finds that the pricing-to-market

actually declines when we move from 10- to 9-digit, 10- to 7-digit, or 10- to 5-digit. Interpreting

Table 4, in the 9-digit case, all categories that are identical up to the first nine digits are aggregated

to construct 9-digit price data. Only 855 commodities are unique up to all ten digits and these are

combined into 338 heterogenous 9-digit categories. As more digits are dropped, the categories be-

come broader and more heterogeneous, more goods are combined into groups, and more observations

can be included in the regressions. For example, at five digits artificial Christmas trees are simply

artificial Christmas trees, while at seven digits these are subdivided into plastic and non-plastic

artificial Christmas trees, one of which may have higher average prices and therefore be considered

higher quality. (The unpublished web appendix contains a random selection of categories and how

they are combined.)

In general, some but not all of the classification distinctions are driven by quality differ-

ences. For instance, olive oil is classified (at the sixth digit) into virgin (150910), refined (150990),

and residue (151000), but knitted cotton sweaters are distinguished (at the ninth digit) by men’s

(611020101) and women’s (611020102) with no obvious quality interpretation. To take our aggre-

gation argument one step further, we identify a number of goods like olive oil, where there is clear

quality variation, and redo the previous exercise. Specifically, we use identifiable quality differences

in terms of freshness, size, purity, stage of processing, price and age (see details in the unpublished

web appendix) to identify 1112 goods that can be paired with at least one more commodity. In

total, we form 455 groupings. The bottom panel of Table 4 reports the results at the disaggregrate

and aggregated levels treating each commodity-year observation separately (hence there are 3492

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aggregated groups rather than 455). Using our disaggregated data we find a pricing-to-market co-

efficient of 0.151 and aggregating to the next level, the coefficient is 0.126. Thus, similar to our full

sample of goods, for this targeted group of goods we also find that this form of aggregation bias

lowers our pricing-to-market estimate.

One possible explanation for this result is that the bias goes the other way; although poor

countries likely consume lower quality goods on average, conditional on importing from the United

States, poor countries may import relatively higher quality goods. Indeed, one possibility is that

since poor countries produce relatively low quality goods to begin with, they have better substitutes

for low quality U.S. exports than other high income countries. That is, the U.S. may have a stronger

comparative advantage in high-quality goods relative to poor countries than relative to other high-

income countries.18,19

While we cannot conclude definitively that measured pricing-to-market in U.S. exports unit

values is not due to quality differences, our various efforts to control for quality suggest that there

is room for pricing-to-market from price discrimination. The model in the next section can be used

to further distinguish the role of price discrimination vs. quality discrimination as an explanation

for the pricing-to-market we find in the data.

D. Variation in PTM by Type of Good

We now examine which types of goods show the strongest pricing-to-market. In particular,

our theory will emphasize search frictions as a source of market power and pricing-to-market, so we

examine whether pricing behavior/unit values differ for goods where search costs may be highest.

18This comparative advantage interpretation of our result for U.S. exports is consistent with Schott (2004), whofinds that U.S. imports coming from lower income countries tended to be less expensive. Since he studies goodsexported from multipe sources into a single market (the U.S.), he attributes this price variation to quality variationrather than PTM. If the U.S. has a stronger comparative advantage in high quality goods production relative to poorcountries, then one would expect U.S. imports from poor countries to be lower quality goods, while its exports arehigher quality.19Another possibility is that per-unit trade costs are relatively higher for poor countries, and hence they import

relatively higher quality goods than in rich countries (see David Hummels and Alexandre Skiba 2004)

13

We measure the importance of search for a good in three ways: (1) distinguishing goods by final

purchasers; (2) method of sale; and (3) distinguishing goods by the importance of repeated trans-

action/long term relationships. For all three, we find that higher search costs are consistent with

more pricing-to-market.

End Use

We first distinguish goods by end use. The opportunity cost of search might also matter to

firms in their decisions to search (see James E. Rauch, 1999, 2001, Alessandra Cassella and James

E. Rauch, 2003, and James E. Rauch and Joel Watson, 2003), but we model consumer search, and

the story applies most naturally to consumers.20

We do indeed find the strongest results for consumer goods. Table 5 reports our coefficients

by end-use category (1-digit codes). Consumer goods have the highest estimated income elasticity

at 0.218. The other four categories (we exclude re-exports and “other”) are all positive but lower

than consumer goods, averaging just 0.130.

Method of Sale

A second way to measure the importance of search costs is to distinguish goods by their

method of sale. To test the role of search frictions on trade flows, Rauch (1999) classifies goods

into three classes: 1) Organized exchange, 2) Reference priced and 3) Differentiated goods. The

Rauch classification is based strictly on the dominant method of sale for goods within a product

category. In principle, price data is most readily available for goods traded on a central exchange

and least available for differentiated goods which require search between suppliers and purchasers.21

The lower panel of Table 5 presents the estimates of pricing-to-market by a good’s mode of sale.

20 In all likelihood, few of these exports are sold directly to consumers. However, the end user is more important thanthe purchaser, since the end user will determine the elasticity of wholesaler demand (see the unpublished appendix).21Tibor Besedes and Thomas J. Prusa (2006) also use the Rauch classification to infer differences in search costs

across goods.

14

We find the highest price-wage elasticity for differentiated goods of 0.163 and the lowest for goods

sold on organized exchanges of 0.074 percent.

While the Rauch classification targets search costs directly, and so this evidence may appear

most direct, there are several caveats. First, the Rauch classification largely picks up differences

in the end-use classification system. Controlling for end-use classification, there are much smaller

differences in pricing-to-market by Rauch classification (Table 5, lower panel). For the most part,

“organized exchange” goods picks up agricultural and industrial supplies while “differentiated”

goods are more likely to be consumer or capital goods. Second, although the classification is based

on method of sale, not the similarity of goods within a product category, more standardized goods

are easier to be traded on organized exchanges or reference priced. Hence, these classifications may

also relate to the heterogeneity (of which quality is only one dimension on which goods differ) of

each good. Indeed, if one expects the law of one price to hold on organized exchanges then the

coefficient here may be troubling, and one might expect that even our organized exchange goods are

highly heterogeneous. However, the third caveat is that the classification is very coarse, classifying

only 1190 categories at the 4-digit SITC level rather than the 10,304 categories at the 10-digit

HS level we use. That is, each category may include HS-10 goods sold in all three manners, but

an organized exchange category should contain relatively more goods sold on organized exchanges,

for example. Finally, with regards to organized exchanges, the fourth caveat is that, even within

Rauch’s “conservative” classification, a large share of these products are not actually transacted

centrally on organized exchanges. Futures are available for these goods, but transactions are purely

financial based on reference prices or price indices over differentiated goods. Indeed, futures are

structured in this way because the commodities are not centrally traded and not standardized.

To address these last three issues, we constructed a finer classification based on actual contract

details that directly maps centrally transacted goods into 10-digit HS goods. We used all 44 goods

15

transacted on U.S. commodity exchanges over the relevant period (see unpublished web appendix

for details). Using this narrow classification, we have 4253 observations. We get a coefficient of

0.023 (with robust standard error of 0.016) on the log wage, which is substantially lower than our

coefficient for the full sample of 0.165, and it is not statistically significant at even the 10 percent

level. Hence, our data measure little to no pricing-to-market for centrally transacted goods. We

interpret this as resulting from a lack of market power because of price availability, but given our

quality caveat, it could also be a result of no heterogeneity among these goods.

Repeated Transactions

Search is likely to be less important when goods are sold as part of repeated transactions or

long term relationships. However, controlling for repeated transactions and long term relationships

is difficult.22

One way is to distinguish, at the good level, which goods are more or less likely to be

sold in repeated transactions. Some goods are commonly made “to order”, according to detailed

customer specifications, and these may be part of a long term relationship that involves repeated

transactions.23 Other goods are commonly produced “to stock”, i.e., without a customer in mind,

and placed directly into inventory. David A. Belsley (1969) and Mark Bils and James Kahn (2000)

note that the latter are likely to have higher inventory/sales ratios, and they classify two-digit SIC

sectors in this way. Another way of making the same distinction is to look at the share of final goods

in total inventory (measured using 1997 Census of Manufactures data for 5- and 6-digits NAICS

industries). If a product is to order then presumably the producer has little incentive to hold goods

in final inventory when there is a customer already in place (indeed the Belsley/Bils/Kahn to stock

22An alternate possibility is that export pricing is due to mismeasurement from transfer pricing considerations byrelated parties. In our working paper (George Alessandria and Joseph Kaboski 2007) we find that controls for transferpricing considerations do not change our estimates.23We thank Steve Davis for suggesting this distinction to us.

16

industries hold about 1/3 more final goods than to order industries). We classify the commodities

with a high share of final inventories (the top quartile) as “to stock” industries.

Table 6 shows that, using all three measures of goods, pricing-to-market coefficients are

higher (0.185 to 0.207) for “to stock goods,” where repeated transactions are less likely. This

is supportive of a role for search, but we also find substantial pricing-to-market for “to order”

goods where repeated transactions are common of 0.146 to 0.160. This may indicate that things

other than search drive pricing-to-market or that, conversely, search may matter even for repeated

transactions. Alternatively, it may indicate that our inventory distinctions are a weak metric for

repeated transactions, perhaps because the distinction for domestic transactions carries over only

weakly to international transactions.

Another way to account for the importance of repeated transactions is to measure and control

for them directly at the customer level. We do this using the monthly U.S. export data. Specifically,

we take one year of data, 1999, and then construct commodity-country unit values for each quarter

within that year. We then estimate pricing-to-market using unit values in the fourth quarter with

controls for the number of quarters with prior transactions,

(3) ln pij = β lnwi + α1I1ij + α2I2ij + α3I3ij + εij ,

where I1ij , I2ij , I3ij , are separate dummies for one, two or three quarters of transactions.

Table 7 reports that with these controls for repeated transactions our pricing-to-market

coefficient falls from 0.215 to 0.194 and that the discount for more frequent buyers is significant,

sizeable, and increasing in the number of previous transactions. A destination that imported from

the U.S. in one previous quarters gets a 4.9 percent discount while a destination that purchases in all

three quarters gets a 34.5 percent discount. That our pricing-to-market estimate is not substantially

17

altered by the presence of large relationship specific discounts suggests that the structure of U.S.

trade relations does not differ dramatically by income. Additionally, the large discounts on repeat

transactions provides some further evidence against the quality variation interpretation of the price

variation as there is no obvious reason to suspect buyers of low quality goods are more likely to be

in long-term relationships.

E. Importance of Pricing-to-Market

Our first aim was to estimate the importance of pricing-to-market for deviations from absolute

PPP. To do so, we modify Engel’s, now standard, decomposition of fluctuations in real exchange

over time to take into account differences in price levels across countries by income,24

pi − p

yi − y=

pTi − pT

yi − y+ (1− α)

¡pNTi − pTi

¢−¡pNT − pT

¢yi − y

,

⇒ εPPP = εLOP + (1− α) εN/T ,(4)

where εPPP is the elasticity of the overall price level (with respect to income per capita), εLOP is

the elasticity of deviations from the LOP (in tradables), εN/T is the elasticity of the relative price of

non-tradables, and α is the share of tradables. This decomposition shows that the aggregate price

level and income relationship we seek to explain, εPPP , depends one-for-one on the deviations from

the LOP and income relationship, εLOP , and only partly on how the relative price of non-tradables

to tradables varies with income across countries, εN/T .

In the data of Figure 1, εPPP = 0.48. The traditional HBS story assumes εLOP = 0 so

that the 100 percent of these deviations from PPP come from the relative price of non-tradables to

tradables. But the data tell us there are sizeable deviations from the LOP. The PWT data on the

24This assumes that the log price index is approximated by a geometric average p = αpT + (1− α) pNT and thatall countries have the same basket.

18

price of tradables indicate that εLOP = 0.31, so that deviations from the LOP account for about

65 percent of the aggregate price-income relationship. The more modest estimates of pricing-to-

market from the export data of εLOP = 0.23 would still account for nearly half of the PPP income

relationship. These findings are consistent with Engel’s finding that about 45 percent of U.S. long-

run real exchange rate fluctuations are due to movements in the relative price of traded goods.25

We interpret the difference between the two values for εLOP (0.31-0.23=0.08) as measuring the 17

percent (0.08/0.48) contribution of local non-traded distribution costs to differences in price levels

across countries.

II Search as a Theory of Pricing-to-Market

This section develops a search-driven theory of pricing-to-market, in which firms charge high

prices on average in countries where wages, and hence the opportunity costs of search, are high.

Consumers in high-wage countries are less willing to spend time searching for low prices. The theory

produces a positive relationship between prices, wages, and income. We first discuss evidence in

support of such a theory and then present a formal model.

A. Corroborating Support for Search

There are a number of reasons to favor the search-based story over a direct preference story

in which consumers become less price sensitive with income. First, there is substantial evidence

within countries that prices are dispersed and that consumers alter their shopping behavior to take

advantage of this dispersion of prices. For instance, Aguiar and Hurst (2007), using scanner data

on consumer expenditures and diary data on time-use, find that a doubling of shopping time lowers

the average purchase price by 7 to 10 percent.26 Second, within countries there is evidence that

25Engel (1999) attributes approximately 95 percent of short-run real exchange rate fluctuations to movements inthe relative price of traded goods.26Shopping with uncertainty, either due to the availability of the goods or time of the shopping trip, is isomorphic

to a model with no uncertainty over search time but uncertainty over prices.

19

shopping effort, measured as time spent shopping per dollar spent, is decreasing in the wage of

shoppers. Third, cross country evidence on time-use suggests that low-income countries have a

comparative advantage in producing non-traded search services. Fourth, empirically, the evidence

from our U.S. export pricing-to-market estimates are consistent with the search story. A final

methodological reason is that the search story offers a true explanation of this relationship, rather

than just assuming it through preferences.

Recall that several pieces of evidence from the U.S. export data are consistent with the

search explanation. First, it is the wage level rather than income per capita that drives the pricing

relationship, when both explanatory variables are included. In the search story, the elasticity is

driven by the opportunity cost of time (i.e., the wage) rather than non-labor income or differences

in income per capita arising from demographic differences. Admittedly, it is possible that the

significance of wages could be driven by other factors, such as measurement quality or coverage of

the wage data (which is strictly the manufacturing wage). Second, goods for which search costs are

highest display the most pricing to market.27

Time-use studies provide evidence that time spent shopping is related to income in a way

consistent with the search model. Many studies have examined the relationship between the op-

portunity cost of time and shopping behavior for consumers within a given economy, i.e., facing a

given distribution of prices. For example, McKenzie and Schargrodsky (2005) study the behavior

of Argentinian shoppers and find a strong relationship in the cross-section of consumers between

consumer search and income. After controlling for quantity purchased, they find that consumers in

27One further piece of suggestive evidence from these data is that high wage countries do not simply pay higheraverage prices; there is also evidence that they face higher dispersion in prices. Specifically, unit value dispersion(calculated as the standard deviation of log unit values across all 10-digit disaggregated HS codes within a higher levelof aggregation, i.e., 9-digit, 8-digit, and 7-digit levels for a given country) in the annual U.S. export data is higher forhigh income countries. The elasticities of log unit value dispersion with respect to log real wages range from 0.041 (for9-digit) to 0.047 (for 7-digit), and these results are marginally significant. Aggregation greatly reduces sample sizes— recall Table 4 — and so t-statistics range from 1.5 to 1.8. When using exchange rate-converted wages rather thanPPP-converted wages, the estimates are somewhat larger and significant even at the 5 percent level.

20

the 10th percentile of the income distribution spend 30 percent more time shopping than consumers

in the 90th percentile. Low-income consumers also visit a greater variety of stores. McKenzie and

Schargrodsky also show that the 2002 Argentine economic crisis, which lowered the wages of work-

ers, led to increases in both these measures of consumer search. Still, financial crises presumably

affect both income/wealth and the distribution of prices, in addition to the opportunity cost of

time. Aguiar and Hurst (2007) have cleaner evidence of the effect of opportunity cost of time. They

document an increase in shopping time per purchase experienced upon retirement, which affects the

opportunity cost of time, but should not affect the lifetime budget constraint nor the distribution

of prices. Both of these studies also find that search effort is negatively related to purchase price.

This evidence of dispersion in prices even within countries provides further support for our search

story over one based on tastes.

The cross-country time-use data are also consistent with our theory. Since the distribution of

prices is not the same over the cross-section of countries, the search story does not (necessarily) im-

ply that consumers in poor countries shop more per unit purchased than consumers in rich countries.

(Indeed, in the model, the response of firm pricing behavior exactly cancels out the increased willing-

ness to search in poor countries, and search time per unit is constant across countries. All differences

in search effort work through the reservation price consumers are willing to accept.) However, our

story hinges on the cost of shopping rising with country income, which requires productivity in the

production technology to rise faster than the productivity in the shopping technology. Since income

(and purchases) rises faster than shopping productivity, a crucial implication of the theory is that

people in rich countries spend more total hours shopping per hour of work than people in poor

countries.

In Table 8 we report the relationship between time-use and income per capita from two

separate cross-country time-use datasets. The first line reports the results from the recently com-

21

pleted European Harmonized Time-Use Survey (EHTUS). The second line reports the results from

the Multinational Time-Use Survey (MTUS). In general, cross-country time-use comparisons are

difficult owing to definitional and sampling differences. The EHTUS was designed with these com-

parability issues in mind, while the MTUS is a collection of mostly individual country surveys that

have been recoded to be more comparable ex-post. Despite these differences, we find that both

surveys generate a similar relationship between the ratio of shopping to work time and income per

capita. From the EHTUS we find a 10 percent increase in income per capita generates a 3.4 percent

increase in the ratio of shopping to work time (3.2 percent in the MTUS).

B. Model

To generate pricing-to-market, exporters must have some market power when selling into a

particular destination and there must be some barriers to international arbitrage. In our framework,

we model many exporters directly selling an identical product directly to consumers. Even though

each exporter sells the same product, the search frictions give each exporter some market power. The

extent of the market power, and thus the properties of the demand curve, is given by the structure

of search. Search also makes international arbitrage costly. For simplicity, we omit a separate retail

and distribution sector, but, we have shown that our results are robust to the inclusion of a separate

retail and distribution sector, where consumers search among retailers that purchase a differentiated

good from producers because producers (and exporters) take into account downstream consumer

search behavior when setting prices to retailers. (See the unpublished web appendix.)

Environment

There are three imperfectly substitutable goods i = {1, 2, 3} and two countries denoted

j = {1, 2}. Goods 1 and 2 are tradables, with good 1 produced exclusively in country 1 and good

2 produced exclusively in country 2. Both countries can produce good 3, but it is not tradable.

22

Including non-tradables along with tradables allows us to incorporate, and distinguish between, the

traditional HBS effect and pricing-to-market.

In each country, there are many stores, each specialized in the sale of a single good. For

simplicity, we assume that the measure of each type of store in each country is predetermined and

the same. Households do not know the price charged at any store and must physically visit a store

to discover its price. Because search takes time and is imprecise, stores have some monopoly power

over consumers and thus may charge different prices for the same good. We assume stores are owned

and operated by the firm producing output, but require no additional inputs. We abstract from

wholesale, retail, and international trade costs since we found them to be only half as important as

pricing-to-market for tradable prices.

Households send out shoppers to search for the lowest price quotes and purchase goods. Each

shopper can buy at most one unit of the good. Shopping therefore takes time away from work and is

imperfect in the sense that consumers do not simultaneously receive price quotes from all the stores

in the market. We model search as noisy, as in Kenneth Burdett and Kenneth L. Judd (1983), so

that a fraction q of shoppers receive a single price quote while the remaining shoppers (1−q) receive

two price quotes. The probability that a shopper receives a single price quote is random and equals

q. After receiving either one or two price quotes, the shopper must decide whether to purchase a

single good at the lowest price quote received or return home empty-handed.

Although without searching agents do not know the price charged at a specific store, they

do know the distribution of prices in the economy. A shopper from country j looking for good i

receives (domestic) price quotes for good i from the known distribution Gij(.). Since the shopper

can buy at most one unit of the good, only the lowest price quote received by a shopper is relevant

23

to the shopper’s purchase decision. The distribution of lowest price quotes is then

Hij (p) = qGij (p) + (1− q)h1− (1−Gij (p))

2i.

From the firm’s perspective, noisy search makes the consumers heterogeneous in that some

shoppers will have only one price quote, while others will have multiple price quotes. Consumers

with multiple price quotes will differ in their second price quote. Since firms cannot distinguish

between these different customers, the price they charge will influence both the profit per sale and

the share of shoppers with multiple price quotes that purchase from them.

Consumer’s Problem

The consumer’s problem is similar to that in George Alessandria (2009). In each country,

there are many identical families. Lowercase variables denote individual decision rules and uppercase

variables denote aggregate decision rules. Each family is composed of a large number of agents,

normalized to a continuum of measure one. The problem of a family is to divide its agents between

working and shopping and to give shoppers instructions on which prices to accept. In country j

the number of agents nij shopping for good i and the number of agents lj working satisfy the time

constraint:

(5)Xi

nij + lj = 1.

It is optimal to send each agent shopping for good i with a reservation price rule to purchase only

if the lowest price quote is below some reservation level, rij . Consumption of good i by country j

consumers depends on both the reservation price and the measure of shoppers. With many shoppers

24

for each good there is no uncertainty in consumption, which equals:

(6) cij = nijHij (rij) .

Given the reservation price, the average purchase price is evaluated from the truncated distribution

of lowest prices:

(7) pij (rij) =

R rij0 pdHij (p)

Hij (rij),

which is clearly increasing in reservation price.

The representative home family chooses reservation prices and shoppers for each good to

solve the following problem:

U j = max{rij ,cij}

U (c1j , c2j , c3j) ,

subject to :

⎧⎪⎪⎨⎪⎪⎩P

i pij (rij) cij = wjlj +Πj ,

equations (5), (6), (7),

where U j is the utility function in country j and Πj is the profits earned by country j firms.

If an interior solution exists the first-order conditions satisfy:

rij =wj

H (rij)+ pij (rij) , i = 1, 2, 3,(8)

U j1

U ji

=r1jrij

, i = 2, 3,(9)

where U ji is the marginal utility of good i.

Equation (8) is an arbitrage condition that implies, at the margin, the family is indifferent

between (1) increasing consumption by purchasing at the reservation price, or (2) sending out

25

additional shoppers, whose opportunity cost of search is measured in terms of the forgone wage,

and purchasing at the average price. With a reservation price of rij , the family expects to send out

1/H (rij) shoppers to purchase a single unit. Since the reservation price is linked to the true cost of

the good, this is the cost that matters at the margin; therefore, the family chooses consumption so

that the marginal rate of substitution between any two goods equals the ratio of their reservation

prices as in equation (9).

We focus on the difference in prices across countries with different incomes and therefore only

consider a representative agent in each country. However, it is straightforward to extend the model

we present to permit heterogeneity in wages. In this case, we see from equation (8) that within

countries, consumers with relatively high wages will have high reservation prices, and search less

intensively, than consumers with relatively low wages, consistent with the within-country evidence.

Firm’s Problem

There are many firms in each country that specialize in the production of either the country’s

tradable or non-tradable good. Firms within a country are ex ante identical. Labor is the only input

into production, and one unit of labor in country j produces aTj units of the tradable good (good j)

and aNTj units of the non-tradable good (good 3). To focus on international price discrimination,

firms can costlessly sell their goods in either country through the pre-established outlets.

To fix ideas, consider the problem of a representative firm in country 1 selling the tradable

good (good 1) in country j. A similar problem exists for non-tradable and country 2 firms. Even

though many firms produce the same good, the search frictions give each firm some monopoly power

and lead firms to behave as monopolistic competitors. Each firm takes as given the distribution of

prices charged by other firms selling the same good, G1j , the number of price quotes that it delivers,

the reservation price of consumers, R1j , and the unit cost of production, w1/aT1 . Given the constant

returns to scale production, the amount of sales does not influence a firm’s unit cost. Thus, the

26

firm’s problem becomes one of maximizing profits per customer that receives a price quote. The

representative firm from country 1 selling in country j solves:

π1j=maxp

µp− w1

aT1

¶Q1j (p) ,

where Q1j (p) is the probability that a firm makes a sale when charging a price p and equals:

Q1j (p)=

⎧⎪⎪⎨⎪⎪⎩q2−q +

2(1−q)2−q [1−G1j (p)] for p≤R1j ,

0 otherwise.

As long as the firm’s price is below the reservation price, the firm will sell to all customers with

one price quote. By increasing its price, the firm increases its revenue per sale but decreases the

likelihood of a sale, since it increases the probability that those customers with two price quotes

have a second price quote that is lower than the firm’s price.

Burdett and Judd (1983) show that given a reservation price, Rij , and cost of production,

wi/aTi , a unique distribution of prices exists, Gij (p) , where

Gij (p) =

⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩0

1− q2(1−q)

Rij−pp−wi/aTi

1

p < P ij

p ∈£P ij , Rij

¤p > Rij

and P ij =2 (1− q)wi/a

Ti + qRij

2− q

Any price on the support of the distribution yields firms the same profits, and firms will randomize.

Firms with relatively high prices primarily sell to those consumers with a single price quote, while

those with relatively low prices attract more of those shoppers with multiple price quotes.

27

Equilibrium

The total demand for labor by firms producing tradables and non-tradables in country j are

LTj and LNT

j , respectively. The labor market clearing condition is:

LTj + LNT

j =Nj1 +Nj2

aTj+

N3j

aNTj

= Lj

A symmetric equilibrium is then a distribution of prices, Gij , and wages, wj ; consumer

decision rules {lj , nij , rij} and aggregate decision rules {Lj , Nij , Rij} in each country j = {1, 2} for

each good i = {1, 2, 3} such that: (1) Given prices, wages, and profits, consumer’s decision rules

solve the household’s problem in each country; (2) Given prices and wages, each firm chooses a price

to solve each firm’s problem; (3) Goods and labor markets clear; and (4) Individual and aggregate

decisions are consistent so that all households from the same country behave identically.

Alessandria (2009) shows that the highest price in the market equals the reservation price.

This upper bound on prices is an equilibrium because the highest-priced firms have no incentive

to charge a price above the reservation price, as they would lose all sales. As no shopper returns

empty-handed, the marginal cost of each good in each country is the average price paid for it plus

the opportunity cost of the shopper. This equals the reservation price:

rij = wj + pij (rij) .

We focus only on the average transacted price (which equals the unit value), since this most

closely corresponds to the measure used by the national statistical agencies and in our empirical

work. Substituting the equilibrium reservation price into the distribution of prices, we can solve for

28

the average price for tradables of good i (from country i) and non-tradables sold in country j as:

(10) pij =wi

aTi+

qwj

1− q.

(11) p3j =wj

aNTj

+qwj

1− q.

The average price for good i paid by a consumer in country j is equal to a markup over the marginal

cost of the firm from country i. The markup depends on both the information structure of search

(summarized by q) and the time cost of search wj . Holding q constant, agents in a country with a

low wage will, on average, pay a lower price than agents in a country with a relatively high wage.

Consequently, the model predicts a strong relationship between prices and local wages.28

III Results

This section evaluates the model’s quantitative properties. We first show that the model

generates the relation between prices, shopping time, and wages within countries documented by

Aguiar and Hurst (2007). We then show that the model generates large deviations from the LOP

across countries even when productivity differences across countries are the same in tradables and

non-tradables. Moreover, we find that our model closely matches the observed relationship between

wages and tradable prices. We then examine the importance of pricing-to-market relative to the

traditional HBS effect arising from productivity differences biased toward tradables.

28Equation (10) clarifies the difference between our model and HBS. In both models, tradables may sell for differentprices across countries. In HBS, the price of tradables may differ internationally when there is a non-traded input,such as wholesale or retail distribution, to get the good to the final consumer. In our model of pricing-to-market, thesearch cost is similar to the non-traded retail or distribution costs in HBS. Unlike in HBS, this search cost is borneby the consumer and through the search frictions it is incorporated into the price charged at the border.

29

A. Calibration

Preferences are consistent with the standard textbook presentation of the HBS model.29

Agents in each country have the following symmetric utility function:

U j = u (c1j , c2j , c3j) =³cρ1j + cρ2j

´αρc1−α3j .

Preferences over tradables and non-tradables are Cobb-Douglas.30 Home and foreign tradables are

often assumed to be perfect substitutes. We depart slightly from this case and set ρ = 0.99.31

The size of the tradable sector is set to match the median trade share of GDP of those OECD

countries for which re-exports are not large32 and for which we have manufacturing wage data from

the BLS. The median country33 imports and exports approximately one-third of GDP in 2000 and

so we set α = 2/3 and non-tradables account for one-third of output.34 The openness of a country

affects the weight we put on the HBS channel but does not substantially change the amount of

pricing-to-market. We report sensitivity to the trade share.

The production side of the economy is calibrated as a symmetric two-country model to

match certain features of the U.S. economy. The production parameters are the search, q, and

market goods, aT , productivities. For our baseline case, we assume that tradable and non-tradable

technologies are identical,35 so that aTj = aNTj = a. Since productivity in market shopping is 1

(each shopper can purchase one unit), a captures the relative productivity of market production to

29See Maurice Obstfeld and Kenneth Rogoff (1996).30The assumption of a unitary elasticity of substition between tradables and non-tradables is consistent with the

estimate of 1.24 by Jonathan Ostry and Carmen Reinhart (1991) for a group of developing countries and EnriqueMendoza’s (1995) estimate of 0.74 for a group of industrialized countries.31Since our focus is on the long-run differences in price levels, our calibration of ρ differs substantially from models

focused on short-run fluctuations.32This requires dropping the Netherlands, Belgium, and Ireland.33For comparison, the median country in the Penn World Tables imported approximately 38 percent of GDP and

exported 42 percent of GDP in 2000.34Alan Stockman and Linda Tesar (1995) use data on a cross-section of OECD countries from 1970 to 1985 and find

the tradable sector is nearly 50 percent of output.35The model is calibrated to the typical good. A more general model would allow for goods to vary in both the

noisy search parameter and the time it takes per purchase, while holding these parameters constant across countries.

30

shopping. In equilibrium, since all produced goods are purchased: a = NL , the ratio of shopping

time to market labor. The American Time-Use Study (2003) reports that the average American

spends about 4 times as much time working as purchasing goods and services, so a = 1/4. The

labor’s share parameter θ is set to 60 percent of total income (Thomas F. Cooley and Edward C.

Prescott 1996), and this pins down q = 0.727. In all of our experiments, we hold this noisy search

parameter constant across countries but allow tradable and non-tradable productivity to vary.36

We use the model to construct a distribution of prices and income, which we then compare

to the data. We do this by solving our two-country model repeatedly. In each case, one country is

the U.S., and the second country is a PWT benchmark country. Productivity in the second country

is chosen to match income per capita relative to the U.S. In this way, we match the world income

distribution and have synthetic price data for 115 artificial economies.

With two symmetric countries, our calibration implies an average markup over marginal cost

of 66 percent. However, because exporters reduce their markup to low-income countries, in the

asymmetric version of the model, the average markup of firms from the richest country is only 60

percent, and 40 percent on average across the 115 countries. Markups are notoriously difficult to

measure, yet this level of monopoly power is consistent with those found in structural IO studies of

the ready-to-eat cereals market (Avi Nevo 2001) and U.S. automobile market (Steven Berry, James

Levinsohn and Ariel Pakes, 1995, and Pinelopi Goldberg, 1995)37. Moreover, our pricing-to-market

evidence finds on average there is a 48 percent price difference for the same goods between the

richest and poorest countries. Such price variation is only possible if markups are of this size.

36The choice of q will determine the markup and will influence the slope of the price-income relation across countries.However, q is calibrated independently of its implications for the slope.37A typical markup in macro papers is about 30 percent (see Michael Dotsey, Robert King and Alexander Wolman,

1999, and Andrew Atkeson and Ariel Burstein, 2008). Estimates of markups from the structural IO literature tendsto find markups that are much higher. For comparison, Berry, Levinsohn, and Pakes (1995) estimate that markupsrange between 31 and 60 percent. Goldberg (1995) which specifically focuses on international trade in cars estimatesmarkups for automobiles are on average 61 percent. Nevo (2001) who studies the ready to eat cereal industry findseven larger markups, ranging from 50 percent to 110 percent.

31

We first consider the results when the productivity gap between countries is the same in both

sectors. This is our Balanced Productivity gap case. In our benchmark, the Biased Productivity

gap case, we assume that productivity difference in the non-tradable sector is smaller than in the

tradable sector. While it is commonly asserted that the productivity gap in tradables is relatively

large compared to non-tradables, there is little direct cross-country evidence of this gap. Studies

that do measure this gap across countries assume that the LOP holds for traded goods and use

relative prices to infer productivity differences.38

Rather than use our theory to construct relative productivity differences, we consider the

evidence on the relationship between income and productivity in tradables and non-tradables, re-

spectively, in the U.S. time series. Dale W. Jorgenson and Kevin J. Stiroh (2000) estimate labor

productivity growth by industry for the U.S. from 1958 to 1996. We split these industries into

tradable and non-tradable sectors and then construct a measure of the productivity gap using each

industry’s share of sectoral value-added. These weighted averages, along with simple averages, of

TFP and labor productivity growth rates39 are reported in Table 9. We find that non-tradable labor

productivity has grown about two-thirds as fast as tradable labor productivity. In the biased pro-

ductivity case, we take the time-series evidence from the U.S. on the productivity gap and examine

the implications of such a gap for the world distribution of income and prices. We also test the

sensitivity to the relative size of this gap. For reference, we also present results from the standard

HBS model with no pricing-to-market.40 Table 10 includes the parameters for the various models.

Prices and income are measured consistently with the empirical data and statistics computed

38For instance, Hsieh and Klenow (2007) use the relative price of consumption to investment to infer that productivityin the investment sector increases with output (in the cross-section) at a rate 2.6 times that of the consumption sector.Similarly, using data on relative price levels, Berthold Herrendorf and Akos Valentinyi (2006) find that the productivitydifference in tradables must be nearly 12 times larger than those in non-tradables.39We follow Mathew Canzoneri et al. (1999) and focus on labor productivity. What really matters for the HBS

effect is the change in the marginal product of labor across sectors. For a broad range of production functions this isproportional to the change in average labor productivity. In contrast, measuring TFP growth depends on the assumedstructure of the production function and requires measures of capital stocks and materials usage.40Our model converges to the HBS model as q → 0 and a becomes large.

32

previously. Deviations from the LOP are measured as the log average price of U.S. exports to

destination j, or lnLOPj = ln (PU.S.,j/PU.S.,U.S.) . To measure income, we follow the convention of

the Penn World Tables and compute nominal GDP, Yj , as the sum of expenditures of domestic

production. The aggregate price level, Pj , is measured using the welfare-based price index.41 Real

income, yj , is nominal GDP deflated by the price index Pj (i.e., yj = Yj/Pj).

With these measures of real income and prices, we estimate statistics that correspond to

our empirical results.42 All results are presented in Table 11. The table’s top panel presents our

elasticity estimates from various versions of the model. The bottom panel decomposes each model’s

price-income relation into its main components. The column titled Data summarizes our estimates

of the price-income relationship from the PWT tables (εPPP and εN/T ) and the U.S. export data

(εLOP and εw), plus evidence from the time-use surveys¡εshop/work

¢.

B. Prices, shopping, and wages within markets

Before considering the cross-country implications of our model, we show the model is con-

sistent, both qualitatively and quantitatively, with some key features of prices paid, shopping time,

and opportunity cost of time within countries documented for U.S. consumers by Aguiar and Hurst

(2007).43 Within countries our model makes two key predictions: first, increasing search lowers

prices paid; and second, increasing the opportunity cost of search lowers search intensity.

With respect to the tradeoff between search and prices paid, Aguiar and Hurst find that a

doubling of shopping time reduces the average price paid by between 7 and 10 percent. While all

agents are identical in our model, we can study the behavior of an individual searches more than the

representative agent by adjusting the wage, and therefore the reservation price, of a single individual

41The price index takes into account only the transaction price of the goods, not the search costs that are borne.Deriving price indices that include the costs of search do not noticeably change the quantitative results. Also, measuringoutput at world prices generates similar results.42We compute a single price for each country and then estimate our statistics from the synthetic sample of countries

running the same regressions we ran in the empirical section.43We thank an anonymous referee for suggesting rigorously analysizing the within country predictions of our model.

33

but keeping the distribution of prices fixed. In our benchmark calibration for the U.S., we find that

a single consumer that shops twice as often as the representative agent, ends up paying 5.5 percent

less on average than the representative consumer.44

With respect to the relation between the opportunity cost of time and search effort, Aguiar

and Hurst present convincing evidence that high opportunity cost individuals search less intensively.

In our model, the opportunity cost of search is linked to the market wage and so we can ask: how

does search time vary with the opportunity cost of time within countries? We find that an agent with

half the median wage searches nearly 20.4 percent more and pays 2.4 percent less than someone with

the median wage. Aguiar and Hurst lack data on wages and instead proxy for the opportunity cost

of time with household characteristics. They find search effort is higher for retired people, single-

earner households, smaller households, and poorer households. Without a precise measure of the

opportunity cost of time, it is difficult to precisely estimate how search effort varies with opportunity

cost of time. However, when looking at different groups by income, an imprecise measure of the

opportunity cost of search, they find high income consumers pay 2.1 percent more and search 16

percent less. Thus, there is strong support for the two key predictions of the model.

Aguiar and Hurst also directly measure the price-income relation within countries. They

find evidence that prices paid increase with income: consumers with income below $30,000 pay 2.1

percent less than those with income above $70,000. Converting these income brackets to averages,

the data suggest a price income relation of about 1.2 percent. In our model, considering a consumer

with half the wage, we find a 3.1 percent price income relation. We make this comparison with

caution, since we do not have a rich model of the relationship between opportunity cost of time and

income in a population cross-section.45

44Generating a larger reduction in prices from search, at the midpoint (8.5 percent) of the Aguiar and Hurst range,requires increasing the opportunity cost of shopping, which we can do by lowering the work to shopping time ratio inhalf and adjusting q to maintain the same labor share (q=0.57).45Aguiar and Hurst results suggest that demographics are important, for example. Another issue is that search

34

Given the small effect of income/wages on prices paid within countries, one might suspect that

our model could only explain a small fraction of the price differences across countries. However,

this logic ignores the general equilibrium effect of firms adjusting prices by market. Specifically,

firms facing a single low wage consumer in a market will not alter their prices in response to this

consumer’s reservation price strategy, but will adjust their prices when facing a market full of low

wage consumers. Consider again a consumer with half the median wage in the U.S.. This consumer

has a 7.4 percent lower reservation price and comes home empty-handed 20.4 percent of the time.

Facing a market full of low wage consumers, however, firms lower their prices in order to attract

more consumers. Consequently, in general equilibrium a representative consumer in a country with

half the median U.S. wage will pay 22.3 percent less than U.S. consumers.46

C. Balanced Technology Gap

In the balanced technology case, the productivity gap across countries is the same in both

sectors, aT1 /aTj = aNT

1 /aNTj . These cross-country productivity differences generate differences in

wages, income and prices. In equilibrium, this generates higher prices for all goods, tradable and non-

tradable, in higher wage/income countries. With tradables accounting for two-thirds of expenditures,

the model generates a quantitatively significant amount of pricing-to-market. The elasticity of

deviations from the LOP with respect to wages is 0.115, which is over 50 percent (0.115/0.209) of

what we observed in the data. Moreover, the elasticities of deviations from the LOP (0.114) and

violations of absolute PPP (0.107) are also substantial in the model. Thus, our model can account

for about half (0.114/0.235) of the deviations from the LOP and almost 25 percent (0.107/0.480) of

the violations of PPP associated with income levels.

technologies may vary across income levels within a country in different ways than they vary across countries. We candiscipline the latter using the time use data, but not the former.46More genereally, these calculations suggest that the distribution of search willingness and efficiency will affect the

prices paid in a market.

35

D. Biased Technology Gap

The column titled Benchmark in Table 11 reports the model’s properties when the relative

productivity of the tradable sector rises with income as in the Jorgensen-Stiroh data. With a biased

productivity gap across countries, the model accounts for 51 percent of the PPP-income relation.

The traditional HBS effect accounts for 28 percent of the price-income relationship, while pricing-

to-market accounts for 23 percent. Pricing-to-market is similar to the balanced productivity case.

For comparison, in the column titled HBS standard model, the HBS model generates only 27

percent of the price-income relationship. Thus, given the observed productivity bias in the time-

series data, the HBS model alone explains little of the PPP-income relationship. Our benchmark

pricing-to-market model exhibits a slightly stronger HBS effect because it generates larger wage

differences than income difference across countries. This occurs because higher market productivity

raises consumption, which leads to more shopping time and less market labor. As income rises, the

ratio of shopping to work time rises faster in our model than the point estimate in the data (0.968

vs. 0.330). Both models generate movements in the relative price of non-traded to traded goods

with income that are only slightly higher than the data.

E. Sensitivity

We now consider the sensitivity of our results to the share of tradables, productivity bias,

labor share of income, and shopping technology.47 Except where noted, the model is parameterized

as in the benchmark case of the biased productivity gap.

47We also explored varying the elasticity of substitution between tradables and non-tradables as well as the elasticityof substitution across tradables. Varying these elasticities primarily affected estimates of εN/T , but had very littleimpact on εLOP or εw. We also explored changing the level of shopping time per purchase equally across countriesand this had a very minor impact on our estimates.

36

Share of Tradables

Figure 3 plots the relationship between the share of tradables and both pricing-to-market

and violations of PPP with balanced productivity. The effect of varying the share of tradables is

minor. This is because pricing-to-market affects all goods, traded and non-traded, in the same way.

Thus, the tradables share only affects pricing-to-market through its influence on the terms of trade

and in turn the relative wage. However, with highly substitutable goods this effect is small.

When the productivity gap is biased, the tradables share has a large effect on the size of

violations from PPP. With a smaller share of tradables, non-traded goods receive a larger weight

in prices. In Table 11, the column titled Low Trade reports the results of the benchmark model

with a trade share of 20.9 percent. This is the necessary tradables share for the benchmark model

to generate the same violations from PPP as in the data. This lower share of tradables slightly

weakens the amount of pricing-to-market in the model.

For comparison, we also include the size of violations from PPP in the standard model with

a low tradables share of α = 0.037 in the column titled HBS Low Trade. This is the level of trade

consistent with the aggregate price-income relationship in the standard HBS model. This tradables

share generates trade flows that are only about 5 percent of those in the data and requires larger

differences in the relative price of tradables to non-tradables than in the PWT data (0.50 vs. 0.41).

Biased Productivity

Figure 4 plots our measures of elasticities against the extent of comparative advantage in non-

tradables (i.e., the ratio of relative non-tradable productivities to relative tradable productivities),

which we denote as gN/T = ln¡aNT1 /aNT

2

¢/ ln

¡aT1 /a

T2

¢. When gN/T = 0, technological differences

are completely concentrated in the tradables sector. When gN/T = 1, there is no relative bias across

sectors in technology levels. For comparison, the elasticity of deviations from PPP in a model

without price discrimination is also reported as εPPP_STD.

37

From Figure 4 we see that the violations from PPP are decreasing in gN/T , while pricing-

to-market is increasing in gN/T . To understand these different results, first note that in the model

without price discrimination, εPPP_STD is decreasing in gN/T because the relative price of non-

tradables is decreasing as the productivity gap diminishes.

Two factors influence the relationship between pricing-to-market and the productivity gap.

First, firms face a lower bound on price in their pricing-to-market decision, since they will never

charge below marginal cost. Thus, pricing-to-market is somewhat non-linear. Among relatively

high-wage countries, firms will vary prices with their customers’ wages, but among relatively low-

wage destinations, markups are already quite low, so firms have very little ability to vary their

price with the destination wage. Second, with a biased productivity gap, relative wage differences

are much larger than relative income differences. This is because relative wages are determined

primarily by the productivity difference in tradables, while relative income differences are based on

productivity in both sectors. Taken together, these two features imply that a biased productivity

gap leads to greater pricing-to-market among high-income locations and lower pricing-to-market

among low-income locations. Given the world distribution of income, the reduced pricing-to-market

to low-income locations has a stronger effect on the estimate of pricing-to-market.

From Figure 4, we see that for the model without pricing-to-market to account for the

violations from PPP, the productivity gap in tradables must be 25 times the productivity gap in

non-tradables, or about 15 times larger than in the U.S. time series data.

Labor Share

We now consider the effect of the labor share on the model’s predictions. In Table 11, the

column titled Low Labor reports the results of the model with a labor share of 50 percent. In

this case, there are larger violations of PPP and these are entirely due to an increase in pricing-to-

market. The lower labor share leads to larger markups and gives firms more room to price-to-market.

38

This is particularly important for pricing to low-income countries since firms will never price below

marginal cost. With higher markups, the model now accounts for almost two-thirds (0.147/0.235)

of the tradable price-income relationship and 75 percent (0.151/0.209) of the tradable price-wage

relationship. Obviously, if we increase the labor share, and lower the average markup, we will weaken

the price-income relation in the model.

Search Time

Our model relies on relative productivity differences in shopping to be smaller than in market

production. As we have seen already, time-use surveys provide evidence of this, but not to the extent

we have assumed. To make the model consistent with the time-use data, we allow the amount pur-

chased per shopping trip to vary across countries with tradable productivity. We assume consumers

in country j can purchase κj units per shopping trip, and let differences in κj be proportional to

the differences in the tradable technology.48 To match the elasticity of shopping to work time, we

set the productivity gap in shopping to be 53 percent of the productivity gap in tradables, so that

lower income countries continue to have a comparative advantage in shopping.

The column titled Variable Shopping reports the results of this modification. The estimates

are quite similar to our benchmark for two reasons. First, because there is less substitution of work

for shopping, we match the income distribution with smaller wage differences. This weakens the

HBS effect. Second, the increased shopping time of lower income countries means that differences

in search costs are smaller for a given difference in wages compared to the benchmark model. This

leads firms to do less pricing-to-market to richer countries, but also allows them to do more pricing-

to-market to poorer countries.49 The net effect is a higher estimate of εLOP that counteracts the

48As before, we normalize the units per purchase in our base country to be κ = 1.49This result may seem perverse but is largely due to estimating a linear model on non-linear data. If we plotted the

distribution of prices against income in the benchmark model and the variable shopping model, we would find that foreach income level the variable search model generates higher prices. However, the variable search model generates analmost linear relationship between income and prices, while the benchmark model generates a non-linear relationship.

39

lower HBS effect, leading to a very small change in the aggregate price-income relationship.

F. Relative Prices and Relative Wages

Pricing-to-market in the model is driven by the opportunity cost of time measured by wages

and not income per capita. As the model abstracts from important determinants of income per

capita such as population growth, labor market participation, and capital accumulation, focusing

on relative wages and prices is a more direct test of the model. Rather than match the distribution

of income per capita, we recalibrate technology to match the exact distribution of relative nominal

wages in the sample of countries for which we have wage data. Figure 5 plots the relationship

between relative price levels and wages from the model and the data.

In the data, the elasticity of price levels with respect to wages, which we denote εPPPw is equal

to 0.41. The model generates εPPPw = 0.30 and thus can explain nearly 75 percent of the relationship

between prices and wages. We find that pricing-to-market is the largest source of the price-wage

relationship, since it accounts for two-thirds of this, while HBS effect accounts for one-third. The

stronger pricing-to-market relationship that we find with wages is consistent with our empirical

result, in which wages seem to drive the pricing-to-market.50

IV Conclusions

Using highly disaggregated data on U.S. exports at the border, we find strong empirical

evidence that pricing-to-market accounts for a substantial amount of the long-run differences in

tradable prices across countries. In turn, these tradable price differences are an important source of

the deviations from absolute PPP, accounting for about 40 percent of the relation between aggregate

price levels and income per capita in the data. This is in stark contrast to the conventional view

that deviations from absolute PPP are solely due to differences in non-traded goods prices.

50Of course, it is also true that since wages are our main focus, this may be due to our rather simplistic modelingof income, which ignored leisure decisions, capital income, etc.

40

Our empirical work suggests that consumers in low-income countries are more price sensitive

than consumers in high-income countries. We develop a model with this type of pricing-to-market

based on international productivity differences and search frictions. Similar to HBS, our model relies

on low-income countries having a comparative advantage in producing non-traded goods. Unlike

HBS, these non-traded goods are shopping activities that affect all prices. Our model generates a role

for local wages in the price-setting behavior of firms and is consistent with cross-country differences

in shopping activities. The model is also consistent with two features of our data analysis suggesting

an important role for search frictions. First, contrary to previous work, we find that wages have

substantially more explanatory power for pricing-to-market than income per capita. Second, pricing-

to-market appears strongest for those goods for which search frictions are likely to be most important,

consumer goods and goods sold in decentralized transactions. This evidence is also consistent with

the within-country evidence that consumers can use search to lower their average purchase price.

Our model thus provides a simple, unified theory of within and across country price dispersion.

Comparing the results of our quantitative analysis and empirical work offers a way to quantify

the magnitude of different sources of international price differences in tradables. Assuming our

model captures all the reasons for pricing-to-market by income, we find that pricing-to-market

(0.109/0.310=35 percent), quality differences ((0.235-0.109)/0.310=41 percent), and downstream

non-traded inputs ((0.310-0.235)/0.310=24 percent) contribute nearly equally in the differences in

tradable prices by income. Naturally, other factors may contribute to the pricing relation we have

found, so further empirical work is necessary. Nevertheless, ours is, to the best of our knowledge, the

first study to document an important empirical and theoretical role for tradable prices in absolute

PPP. It is typically assumed in theoretical and empirical work that the LOP holds for tradables.

We have shown that such an assumption drastically overstates the differences in productivity across

sectors across countries and matters for understanding the source of income differences as well.

41

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44

Appendix A - Random Sample of 10 Goods

Consumer/Automotive Goods

• Alarm clocks, not battery or AC powered• Men’s and boys’s weaters of cotton, knitted or crocheted containing ge 36 percent by weightof flax fiber

• Pocket lighters, gas fueled, refillable• Table or kitchen glassware other than drinking glasses, having a linear coefficient of expnsnnov 5X0-6/Kelvin in temperature range of 0 to 300 deg C

• Washing machines, except coin operated, fully automatic, dry linine capacity not exceeding10 kg, household or laundry type

Non-Consumer Goods (Agriculture, Industrial, and Equipment)

• 4,4’-Isopropylidendicyclohexanol; & Mixtures cont less than 90% by weight of stereoisomersof 2-Isopropyl-5-Methylcylohexanol, but not more than.

• Grinders, polishers and sanders, suitable for metal working, rotary type (inc combined rotary-percussion) pneumatic tools for working in the hand

• Monolithic I/C’s, digital, silicon, (MOS), volatile memory, static read-write random access(SRAM) over 300,000 bits

• Peanuts, blanched• Synthetic filament yarn except sewing thread, not for retial sale, single, multifilament, with atwist of GE turns per M of polyethylene, propylene

45

Figure 1: Consumption Price Levels and Real GDP per Capita

ALBARG

ARM

ATGAUS

AUT

AZE

BEL

BEN

BGD

BGR

BHR BHS

BLRBLZ

BMU

BOLBRA

BRB

BWA

CAN

CHE

CHL

CIVCMR

COG

CZE

DMA

DNK

ECU

EGY

ESP

EST FIN

FJI

FRA

GAB

GBR

GEO

GER

GIN

GRC

GRD

HKG

HRVHUN

IDN

IRL

IRN

ISL

ISR

ITA

JAM

JOR

JPN

KAZKEN

KGZ

KNA

KOR

LBN

LCA

LKA

LTU

LUX

LVA

MAR

MDA

MDG

MEX

MKD

MLI MNG

MUS

MWI

NGA NLD

NOR

NPL

NZLOMN

PAK PAN

PER

PHL

POL

PRT

QAT

ROM

RUS

SEN

SGP

SLE

SVK

SVN

SWE

SWZ

SYR

THA

TJK

TKM

TTO

TUN

TURTZA

UKR

URY

USA

UZB

VCT

VEN

VNM

YEM

ZMB

ZWEy = 0.48x - 4.56

R² = 0.49

-2

-1.5

-1

-0.5

0

0.5

1

1.5

6 7 8 9 10 11

Log Real GDP per Capita

Log

Pri

ce o

f Con

sum

ptio

n

(Source: Penn World Tables 6.1, ICP 1996 Benchmark Price Data)

Figure 2: Tradable Consumption Prices and Real GDP per Capita

ALB

ARG

ARM

ATG AUS

AUT

AZE

BEL

BEN

BGD

BGR

BHR

BHS

BLR

BLZ

BMU

BOL

BRA

BRB

BWACAN

CHE

CHL

CIVCMR

COG CZE

DMA

DNK

ECU

EGY

ESP

EST

FINFJI

FRA

GAB

GBR

GEO

GER

GIN

GRC

GRD

HKG

HRV

HUN

IDN

IRL

IRN

ISLISR

ITA

JAM

JOR

JPN

KAZKENKGZ

KNA

KOR

LBN

LCA

LKA

LTU

LUX

LVA

MAR

MDAMDG

MEX

MKD

MLI

MNG

MUS

MWI

NGA

NLDNOR

NPL

NZLOMN

PAKPAN

PER

PHL

POL

PRT

QAT

ROM

RUSSEN

SGP

SLE

SVK

SVN

SWE

SWZ

SYR

THA

TJK

TKM

TTO

TUN

TUR

TZA

UKR

URY

USA

UZB

VCTVEN

VNM

YEM

ZMB

ZWE

y = 0.31x - 2.92R² = 0.39

-2

-1.5

-1

-0.5

0

0.5

1

1.5

6 7 8 9 10 11

Log Real GDP per Capita

Log

Pri

ce o

f Tra

dabl

e C

onsu

mpt

ion

(Source: Penn World Tables 6.1, ICP 1996 Benchmark Price Data)

Figure 3: Price Elasticities and Tradable Share

0.08

0.1

0.12

0.14

0 0.2 0.4 0.6 0.8 1

Tradable share (�)

Ela

stic

ity

�PPP

�LOP

�W

Figure 4: Price Elasticities and Productivity Gap

0.00

0.25

0.50

0.75

0 0.2 0.4 0.6 0.8 1

Productivity gap (gN/T)

Ela

stic

ity

�LOP �W

�PPP

�PPP_STD

Figure 5: Relative Prices and Wages

PjModel = 0.30wj

Model + 0.01

PjData = 0.41wj

Data + 0.18

-2

-1

0

1

-4 -3 -2 -1 0 1

Log (Wi/WU.S.)

Log

(Pi/P

U.S

.)

Model Data

Coefficient GDP per Capita only Wage only Both together

Log GDP per capita 0.235(4.9) - 0.041

(1.4)

Log Wage - 0.209(7.1)

0.188(8.1)

Observations 240245 240245 240245Groups 5613 5613 5613

Table 1: Coefficients from Commodity-Year Fixed-effects Regressions ofLog Unit Values on Log real GDP per capita and/or Log Wages

t-statistics are based on country-year clustered White robust standard errors.

(tstatistics in parentheses)

Variable All Small quality differences

Large quality differences

Smallest quality differences

Interacting quality differences

Log Wage 0.159 0.128 0.183 0.107 0.084(5.7) (6.2) (5.2) (5.4) (4.7)

Observations 704121 296186 407935 44552 704121Groups 49513 24757 24756 4951 49513

Mean quality 1.44 0.78 1.92 0.29 1.44

(tstatistics in parentheses)

Based on those HS codes that are both imported and exported in the same year. For each commodity (a year hs code) quality variation is measured as the standard deviation of ln import unit values from all sources. For columns 2 and 3, goods with smallquality differences have a standard deviation of prices of less than 1.21 and goods with large quality differences have a standarddeviation greater than 1.21. For column 4, goods with the smallest quality differences have a standard deviation of unit values of less than 0.46. We run the regression from equation 1 on these seperate groups with good fixed effects. The final column reportsthe results of the regression in equation 2 that includes an interaction of quality and relative income. The row Mean quality reportsthe observation weighted mean quality of each sample. t-statistics are based on country-year clustered White robust standard errors.

Table 2: PTM and "Quality" Variation using Import Prices

Monthly-hs

Variable\grouping port-hs-month port-hs-year hs-month hs-yr port-hs-yr hs-yr hs-month hs-yr

hs-yr, no additionalcontrols

Log Wage 0.096 0.087 0.085 0.082 0.085 0.081 0.148 0.112 0.184(2.8) (2.6) (3.1) (3.1) (3.4) (5.8) (12.6) (4.2) (2.8)

Observations 3532393 3532393 3532393 3532393 848432 848432 1322053 217707 217707Groups 1753642 289895 170184 15083 289895 15083 87954 15083 15083

Table 3 : Export Prices and Wages Using Monthly Data from 1998 and 1999

(tstatistics in parentheses)

Notes: Includes separate controls for share of trade (value) shipped by air and ln number of shipments; t-statistics are based oncountry-year clustered White robust standard errors.

Monthly-port data Annual port Annual-hs

Number of Commodity Groupings Number of Observations Coefficient

Individual Commodities 855 74264 0.184(6.3)

Aggregated Commodities 338 48552 0.158(5.0)

Individual Commodities 4186 459542 0.150(5.9)

Aggregated Commodities 1155 209972 0.115(3.8)

Individual Commodities 7358 861030 0.164(6.1)

Aggregated Commodities 1490 320013 0.134(4.4)

Individual Commodities 7593 88340 0.151(7.6)

Aggregated Commodities 3492 51152 0.126(6.2)

Notes: For Panel B there are 1112 separate commodities that are grouped in 455 groups. t-statistics are based on country-year clustered White robust standard errors.

Panel B: Commodities Grouped by Identifiable Quality Differences

Table 4: Effect of Quality Aggregation on Coefficients from Regressions of Log Prices on Log Real Wages

Combined at the 9-digit level

Combined at the 7-digit level

Combined at the 5-digit level

Panel A: All Commodities

(tstatistics in parentheses)

All Goods Foods, feeds, and beverages (EU=0)

Industrial supplies and materials

(EU=1)

Capital goods, except automotive

(EU=2)

Auto, vehicles, parts and engines (EU=3)

Consumer goods (EU=4)

Log Wage 0.164 0.091 0.176 0.143 0.11 0.218(5.9) (5.2) (5.7) (4.3) (3.6) (7.4)

Observations 1125186 104774 464314 308485 24715 215530

Log Wage 0.074 0.042 0.110(3.2) (2.3) (3.5)

Observations 38865 19656 19209

Log Wage 0.146 0.107 0.158 0.378 0.152(5.3) (5.9) (5.0) (4.5) (6.0)

Observations 204681 48810 148388 790 6693

Log Wage 0.163 0.096 0.176 0.123 0.095 0.221(5.6) (5.8) (5.1) (4.1) (2.8) (7.7)

Observations 547594 29291 159797 185027 15148 153673

Notes: t-statistics are based on country-year clustered White robust standard errors. Rauch classification based on conservativeclassification scheme.

Table 5: PTM By Enduse Category and Rauch Classification

Rauch = "w" - "goods traded on an organized exchange (homogeneous goods)"

Rauch = "r" - "reference priced goods"

Rauch = "n" - "differentiated goods"

By Rauch Classification and End-use

(tstatistics in parentheses)

To Order (Belsley)

To Stock (Belsley)

To Order(Bils & Kahn)

To Stock(Bils & Kahn)

Final good shareof inventory

(bottom quartile)

Final good share of inventory

(top quartile)

Log Wage 0.160 0.185 0.153 0.207 0.146 0.191(5.0) (7.6) (5.0) (8.1) (4.9) (8.1)

Observations 651595 318129 700885 268839 266007 237294

Final good inventory share 0.354 0.518 0.371 0.503 0.240 0.600

Table 6: Role of Inventory Holdings for Pricing-to-Market

Belsley (1969) classifies 6 2-digit SIC industries as more likely to produce to stock. The sectors are: food and kindred products,tobacco, apparel and other textile products, chemicals and allied products, rubber, and plastic products. Bils and Kahn (2000) modify Belsley by shifting food into to order and lumber to stock. Inventories are measured at the 6-digit NAICS level (except for5 industries at the 5-digit level) using the 1997 Census of Manufacturers. The share of final inventories measures the finishedinventories divided by total inventory holdings (where inventory measures are an average of beginning- and end-of-year holdings).

(tstatistics in parentheses)

Variable Whole yr (99) 99Q4 99Q4

Log Wage 0.229 0.215 0.194(2.5) (2.4) (2.7)

1 previous transaction -0.049(2.0)

2 previous transactions -0.079(3.0)

3 previous transactions -0.345(6.6)

Observations 298460 75609 75609

Table 7: Pricing-to-market and Repeated Transactions

Notes: A previous transaction is a quarter with a shipment to a country. Dummies for the number of previous transactions are based on the number of quarters in the first 3 quarters of the year with transactions. t-statistics are based on country-year clustered White robust standard errors. Rauch classification based on conservative classification scheme.

(tstatistics in parentheses)

Group Observations Shop/Work Time Work Time* Shop Time**

0.337 -0.139 0.198(2.8) (-2.0) (2.8)0.321 -0.112 0.208(4.3) (-2.7) (3.1)

** Shop time is measured as time shopping and receiving personal services plus time travelling to shopping.

MTUS 48

EHTUS countries: Belgium, Estonia, Finland, France, Germany, Hungary, Italy, Latvia, Lithuania, Norway, Poland, Slovenia, Spain, Sweden, U.K. and sample is 20 to 74 year olds. MTUS countries: Canada (71, 81, 86, 92, 98), Denmark (64, 87) France (65, 74, 98), Netherlands (75, 80, 85, 90, 95, 00), Norway (71, 81, 90, 00), U.K. (61, 75,83, 87, 95,00), USA (65, 75, 85, 92, 98, 03), Hungary (65, 77), West Germany (65), Poland (65), Belgium (65), Bulgaria (88), Czechslovakia (65), East Germany (65), Yugoslavia (65), Italy (80, 89), Australia (74), Israel (92), Germany (92), Austria (92), S. Africa (00), Slovenia (00) and the sample is 20 to 59 year olds.

* EHTUS work time is measured as paid work in primary and secondary employment. MTUS work time is measured as paid work in first and second job plus paid work at home.

Table 8: Coefficient from Regression of Log Time Use on Log GDP per capita(t-statistics in parentheses)

EHTUS 15

LaborProductivity

Tradables 0.56 1.85 0.67

Non-Tradables 0.27 1.60 0.26

Ratio (gN/T) 0.48 0.87 0.38

Non-tradables include: Construction; Transport and Warehouse; Communications; Electric Utilities; Gas Utilities; Trade; FIRE; Services.

*The weighted measure weights productivity growth in each sector by its average annual share of value added in either the tradable or non-tradable sector. The productivity data is reported in Jorgenson and Stiroh (2000). Total Factor Productivity Growth (TFP) is measured as a residual using materials, capital stocks, and labor used plus their expenditure shares.

2.07

1.41

0.68

Tradables include: Agriculture; Metal Mining; Coal Mining; Petroleum and Gas; Nonmetallic Mining; Food Products; Tobacco Products; Textile Mill Products; Apparel and Textile; Lumber; Furniture; Paper Products; Printing and Publishing; Chemical Products; Petroleum Refining; Rubber and Plastics; Leather Products; Primary Metals; Fabricated Metals; Industrial Machinery and Equipment; Electronic and Electric Equipment; Motor Vehicles; Instruments; Miscellaneous Manufacturing; Other Transportation Equipment; Stone, Clay and Glass.

Table 9: U.S. Sectoral Productivity Growth (1958-96)

Average Growth Weighted Avg* Growth

TFP TFPLabor

Productivity

ParametersBenchmark Model

Technology �=1/4, q=0.727, ln(ajNT/�)/ln(aj

T/�) = 2/3Preferences �=2/3,�=0.99

VariationsBalanced ln(aj

NT/�)/ln(ajT/�) =0

Low Trade Share �=0.209Low Labor Share q=0.8, �=1/4Vary Shop (�j

NT/��j)/(ajT/�) = 0.53

HBS Model q=0.00005, �=1/4Standard �=2/3,�=0.99Low Trade �=0.037

MeasurementNominal Income Yj=Pj1(Rj1)Nj1+Pj2(Rj2)Nj2+Pj3(Rj3)Nj3

Aggregate Prices Pj=(PTj/�)�(P3j/(���))���, Pj

T = ((P1j)�����+( P2j)

�����)�����

Empirics ln Pj = �PPPlnyj+ej

ln LOPj = �LOPlnyj+ej

ln LOPj = �wlnwj+ej

ln PjNT/Pj

T = �N/Tlnyj+ej

Table 10: Parameter Values and Measurement

Balanced Low Labor Variable Low Trade Low Trade

Data PTM Benchmark share = 1/2 Shopping �=0.209 Standard �=0.037

�PPP 0.480 0.107 0.245 0.283 0.232 0.480 0.128 0.430

�LOP 0.235 0.114 0.109 0.147 0.117 0.111 0.000 0.000

�w 0.209 0.115 0.111 0.151 0.115 0.115 0.000 0.000

�N/T 0.408 -0.022 0.406 0.410 0.345 0.467 0.384 0.498

�shop/work 0.330 1.041 0.968 0.962 0.332 1.001 0.988 1.042

Fraction of �PPP 22% 51% 59% 48% 100% 27% 90%

Fraction from PTM 24% 23% 31% 24% 31% 0% 0%

Fraction from HBS -1% 28% 28% 24% 69% 27% 90%

*�PPP and �N/T are based on the whole sample of 115 PWT Benchmark countries while �w and �LOP are based the 28 benchmark countries for which the BLS provides wage data.

**The variations of the Benchmark economy all include a biased productivity gap. In the HBS economies there is no pricing-to-market but consumers do shop for goods. Low labor share is the Benchmark economy with labor share of income of 1/2. The Variable Shopping economy is one in which the shopping technology improves along with the tradable technology. The Low Trade Share economy is the Benchmark economy with a lower tradable shareof 0.209. The HBS Low Trade is the HBS model with a low trade share of 0.037.

Table 11: Model Results

Variations on Biased Productivity Economies**

PTM Model HBS Model

A. Elasticity*

B. Accounting for violations from PPP